Optimal monetary policy in open economies

Transcription

1 Optimal monetary policy in open economies Giancarlo Corsetti European University Institute, University of Rome III and CEPR Luca Dedola European Central Bank and CEPR Sylvain Leduc Federal Reserve Bank of San Francisco June 21 To appear in the Handbook of Monetary Economics, Vol. III, edited by Benjamin Friedman and Michael Woodford. We thank for helpful comments our discussant Pierpaolo Benigno, and Charles Engel, Jordi Galì, Katrin Rabitsch, Assaf Razin, Yusuf Soner Baskaya and Michael Woodford, and seminar participants at the ECB s Conference on Key Developments in Monetary Economics, held in Frankfurt on Oct 29-3, 29, and the Federal Reserve Bank of New York. We thank Ida Maria Hjiortso and Francesca Viani for excellent research assistance. Financial support by the Pierre Werner Chair Programme at the Robert Schuman Centre of the European University Institute is gratefully acknowledged. The views expressed in this paper do not necessarily re ect those of the ECB or the Federal Reserve System. 1

2 Abstract This chapter studies optimal monetary stabilization policy in interdependent open economies, by proposing a uni ed analytical framework systematizing the existing literature. In the model, the combination of complete exchange-rate pass-through ( producer currency pricing ) and frictionless asset markets ensuring e cient risk sharing, results in a form of open-economy divine coincidence : in line with the prescriptions in the baseline New- Keynesian setting, the optimal monetary policy under cooperation is characterized by exclusively inward-looking targeting rules in domestic output gaps and GDP-de ator in ation. The chapter then examines deviations from this benchmark, when cross-country strategic policy interactions, incomplete exchange-rate pass-through ( local currency pricing ) and asset market imperfections are accounted for. Namely, failure to internalize international monetary spillovers results in attempts to manipulate international relative prices to raise national welfare, causing ine cient real exchange rate uctuations. Local currency pricing and incomplete asset markets (preventing e cient risk sharing) shift the focus of monetary stabilization to redressing domestic as well as external distortions: the targeting rules characterizing the optimal policy are not only in domestic output gaps and in ation, but also in misalignments in the terms of trade and real exchange rates, and cross-country demand imbalances. Keywords: Currency misalignments, demand imbalances, pass-through, asset markets and risk sharing, optimal targeting rules, international policy cooperation JEL codes: E44, E52, E61, F41, F42 2

3 1 Introduction and overview Research in the international dimensions of optimal monetary policy has long been inspired by a set of fascinating questions, shaping the policy debate in at least two eras of progressive cross-border integration of goods, factors, and assets markets in the years after World War I and from Bretton Woods to today. Namely, should monetary policy respond to international variables such as exchange rates, global business cycle conditions, or global imbalances beyond their in uence on the domestic output gap and in ation? Do exchange rate movements have desirable stabilization and allocative properties? Or, on the contrary, should policymakers curb exchange rate uctuations and be concerned with, and attempt to correct, currency misalignments? Are there large gains the international community could reap by strengthening cross-border monetary cooperation? In this chapter, we revisit these classical questions by building on the choice-theoretic monetary literature encompassing the research agenda of the New Keynesian models (see, e.g., Rotemberg and Woodford 1997), the New Classical Synthesis (see, e.g., Goodfriend and King 1997), and especially the New Open Economy Macroeconomics, henceforth NOEM (see, e.g., Svensson and van Wijnbergen 1989, Obstfeld and Rogo 1995). In doing so, we will naturally draw on a well-established set of general principles in stabilization theory, which go beyond open-economy issues. Yet, the main goal of our analysis is to shed light on monetary policy trade-o s that are inherently linked to open economies which engage in cross-border trade in goods and assets. A general feature sharply distinguishes monetary policy analysis in open economies from its closed-economy counterpart. This consists of the need to account explicitly for di erent forms of heterogeneity that naturally arise in an international context, ranging from instances of ex ante heterogeneity across countries such as product specialization, cross-country di erences in technology, preferences, currency denomination of prices, nancial market development, and asset holdings, to ex post heterogeneity such as the asymmetric nature of shocks, as well as endogenous redistributions of wealth across countries in response to shocks. While these forms of heterogeneity enlarge the array of potential policy trade-o s relevant to the analysis, in a global equilibrium monetary policy problems are addressed using as many policy instruments as there are monetary authorities in the model economy. Along this dimension as well, however, there could be heterogeneity in objectives and policy strategies. Building on an open-economy model which has been the workhorse for 3

4 much of the literature featuring two countries, each specialized in the production of a type of goods in di erent varieties 1 we study optimal monetary policy under alternative assumptions regarding nominal rigidities and asset market structure, adopting the linear-quadratic approach developed by Woodford (23). A rst important result consists of deriving a general expression for the open-economy New Keynesian Phillips curve, relating current in ation to expected in ation and changes in marginal costs. In an open economy, the latter (marginal costs) is a function of output gaps plus two additional terms, one accounting for misalignments in international relative prices, the other for ine cient uctuations in aggregate demand across countries. In analogy to the de nition of output gaps, we measure misalignments in terms of deviations of international relative prices from their rst-best levels. 2 The term accounting for ine cient uctuations in aggregate demand instead measures relative price- and preference-adjusted di erentials in consumption demand, which generally di er from zero in the presence of nancial market frictions. This tripartite classi cation of factors driving the Phillips curve output gaps, international relative price gaps, and cross-country demand imbalances also provides the key building block for our policy analysis. Indeed, a second important result is that, together with in ation rates, the same three factors listed above are the arguments in the quadratic loss functions which can be derived for di erent speci cations of our workhorse model. Of course, the speci c way these arguments enter the loss functions vary across model speci cations, re ecting di erent nominal and real distortions. A well-known result from monetary theory is that stabilization policy should maintain in ation at low and stable rates, as a way to minimize the misallocation of resources due to staggered nominal price adjustment. In the baseline model with only one sector and one representative agent, 1 The model, similarly to Chari et al. (22), can be seen as a monetary counterpart to the international real business cycle literature after Backus, Kehoe and Kydland (1994), and, for versions including nontraded goods, Stockman and Tesar (1995). For recent evidence on monetary models of exchange rates see Engel et al. (27). 2 We stress that, conceptually, the e cient exchange rate is not necessarily (and in general will not be) identical to the equilibrium exchange rate, traditionally analyzed by international and public institutions, as a guide to policy making. Equilibrium exchange rates typically refer to some notion of long-term external balance, against which to assess short-run movements in currency values (see e.g. Chinn 21). On the contrary, the e cient exchange rate is theoretically and conceptually de ned at any time horizon, in relation to a hypothetical economy in which all prices are exible and markets are complete, in strict analogy to the notion of a welfare relevant output gap. In either case, the assessment of e cient prices and quantities, at both domestic and international levels, posits a formidable challenge to researchers. 4

5 such misallocation takes the form of price dispersion for goods which are symmetric in preferences and technology. In such a model, optimal monetary policy is characterized by a exible in ation target, trading o uctuations in the GDP de ator and the output gap vis-à-vis ine cient shocks such as markup shocks (which would not be accommodated by the social planner). Conversely, the optimal target will result in the complete stabilization of the domestic GDP de ator and output gap, vis-à-vis e cient shocks such as disturbances in productivity and tastes (which would be accommodated by the social planner) see, e.g., Galí (28) or Woodford (23). As a rst step in our study, we consider a speci cation of the workhorse model for which the prescription guiding optimal monetary policy is identical to the one for the benchmark economy mentioned above: optimal policy is isomorphic to the one for baseline closed-economy models; see, e.g., Clarida Galí and Gertler (22), henceforth CGG, and Benigno and Benigno (26), henceforth BB. For this to be the case, it is crucial that endogenous movements in the exchange rate correct potential misalignments in the relative price between domestic and foreign goods in response to macroeconomic shocks, in accord with the classical view of the international transmission mechanism as formalized by, e.g., Friedman (1953). Underlying the classical view, there are two key assumptions. First, frictionless asset markets provide insurance against all possible contingencies across borders. Second, producer prices are sticky in domestic currency, so that the foreign currency price of products move one-to-one with the exchange rate the latter assumption is commonly dubbed producer currency pricing (henceforth PCP) by the literature. By virtue of perfect risk insurance and a high degree of exchange rate pass-through of import prices, as stressed by Corsetti and Pesenti (25) and Devereux and Engel (23), preventing price dispersion within categories of goods automatically corrects any possible misalignment in the relative prices of domestic and foreign goods a form of divine coincidence, in the de nition of Blanchard and Galí (27). In relation to this baseline speci cation, the rest of our analysis calls attention to open-economy distortions which break the divine coincidence just de ned thus motivating optimal target rules explicitly featuring openeconomy variables. In a closed-economy context, the divine coincidence breaks down in models including both price and wage rigidities, or price rigidities in multiple sectors in which case the trade-o is between stabilizing relative prices within and across categories of goods and services, see, e.g., Erceg et al. (2) or introducing agents heterogeneity, whereas policy trade-o s may then arise because of imperfect risk insurance, see, 5

6 e.g., Curdia and Woodford (29). Analogous trade-o s naturally and most plausibly arise in open economies in the form of misalignments in the terms of trade (the relative price of imports in terms of exports) or the real exchange rate (the international relative price of consumption), as well as in the form of cross-border imbalances in aggregate demand. At the core of the policy problem raised by misalignments and imbalances however lies the exchange rate in its dual role of relative price in the goods and the asset markets which has no counterpart in a closed-economic context. In addition, ine ciencies and trade-o s with speci c international dimensions result from cross-border monetary spillovers when these are not internalized by national monetary authorities i.e., when these act noncooperatively in setting their domestic monetary stance. Except under very special circumstances, all these considerations rule out isomorphism/similarities in policy prescriptions in closed and open economies. Under the maintained assumption of complete markets, in the rst part of the chapter we characterize optimal monetary policy in the presence of distortions resulting either from nominal rigidities causing the same good to be traded at di erent prices across markets, or from national policymakers failure to internalize international monetary spillovers. In the second part of the chapter, we instead reconsider the optimal policy in an incomplete market framework, focusing on the interactions between nominal and nancial distortions. 3 We highlight below the main results of the chapter. Skepticism of the classical view: local-currency price stability of imports In contrast with the classical view, recent leading contributions have emphasized the widespread evidence of local-currency stability in the price of imports, attributing asigni cant portion of it to nominal rigidities. In the data, exchange rate movements appear to be only weakly re ected in import prices (a large body of studies ranges from those surveyed by Goldberg and Knetter 1997, to recent work based on individual goods data, such as Gopinath and Rigobon 28). Under the assumption that import prices are sticky in the local currency a hypothesis commonly dubbed local currency pricing or LCP by the literature the transmission of monetary policy is fundamentally di erent relative to the classical view. Namely, with LCP, exchange rate movements have a limited impact on the price of imports faced by consumers pass- 3 For a thorough analysis of the international dimensions of monetary policy, including issues in macroeconomic stabilization in response to oil shocks and in monetary control in a globalized world economy, see the excellent collection of contributions in Galí and Gertler (29). 6

7 through is incomplete. Rather, they cause widespread ine cient deviations from the law of one price: identical goods trade at di erent prices (expressed in the same currency) across national markets. Exchange rates cannot realign international and domestic relative prices at their e cient level. In the last few years, the debate contrasting the international transmission mechanism and policy analysis under PCP and LCP has arguably been the main focus in the early NOEM literature (see, e.g., the discussion in Obstfeld and Rogo 2, Betts and Devereux 2, and Engel 22). With LCP, there is no divine coincidence since cross-country output gap stabilization no longer translates into relative price stabilization. In response to productivity shocks, for instance, stabilizing marginal costs of domestic producers neither coincides with stabilizing their markups in all markets, nor it is su cient to realign international prices. As shown by Engel (29), the optimal policy thus will have to trade o internal objectives (output gaps and an in ation goal) with correcting misalignments. Speci cally, similar to the PCP case, under LCP cooperative policymakers dislike national output gaps and in ation, as well as cross-country di erences in output, to the extent that these lead to misalignments in international relative prices. Yet, relative to the PCP case, the in ation rates relevant to policymakers are di erent for domestic goods than for imports. The di erent terms in in ation re ect the fact that, with LCP, policymakers are concerned with ine ciencies in the supply of each good due to price dispersion in the domestic and in the export destination markets. In addition, the policy loss function includes a new term in deviations from the law of one price, driving misalignments in relative prices and causing ine ciencies in the level and composition of global consumption demand, a point especially stressed by the literature assuming one-period preset prices; see Devereux and Engel (23) and Corsetti and Pesenti (25). The targeting rules characterizing optimal policy under LCP are generally complex, involving a combination of current and expected values of domestic variables, like the output gap and producer and consumer prices, as well as of external variables, like the real exchange rate gap. Nonetheless, they considerably simplify under two alternative conditions, that is, either the disutility of labor is linear a case stressed by Engel (29) or purchasing power parity (PPP) holds in the rst best a case discussed by the early contributions to the NOEM literature such as CGG and BB. We show that either condition leads to the same clear-cut optimal policy prescriptions: in the face of e cient shocks policymakers should completely stabilize CPI in ation, the global output gap, and the real exchange rate gap at the expense of terms of trade misalignments and understabilization 7

8 of relative output gaps. This implies complete stabilization of consumption around its e cient level and, only when PPP holds, complete stabilization of nominal exchange rates. The two special cases of PPP and linear disutility of labor are noteworthy, in light of the attention they receive in the literature and their analytical tractability. Yet, the strong policy prescriptions derived from their analysis should not be generalized. Indeed, the main lesson from the LCP literature is that policymakers should pay attention to international relative price misalignments, as the exchange rate cannot be expected to correct them according to the classical view, and to consumer price in ation, since with sectoral di erences in in ation there are both supply and demand distortions. In general, however, it motivates neither complete stabilization of the CPI index, even in the face of e cient shocks, since the optimal trade-o in stabilizing di erent components of CPI in ation do not necessarily coincide with CPI weights, nor curbing exchange rate volatility under the optimal policy, exchange rate and terms of trade volatility can remain quite high under LCP. Competitive devaluations and strategic interactions Policy tradeo s with an international dimension are also generated by cross-border spillovers in quantities and prices when these give rise to strategic interactions among policymakers one of the main topics of traditional policy analysis in open economies (see, e.g., Canzoneri and Henderson 1991 and Persson and Tabellini 1995). This chapter revisits classical concerns about competitive devaluations in a modern framework, providing an instance of a game between benevolent national monetary authorities, each attempting to exploit the monopoly power of the country on its terms of trade to raise national welfare. Drawing on the literature, we focus on a Nash equilibrium assuming complete markets and PCP. Depending on whether goods are complements or substitutes in preferences, domestic policymakers have an incentive to either improve or worsen their country s terms of trade, at the cost of some in ation. These results appear to support the notion that strategic terms of trade manipulation motivates deviations from domestic output gap stabilization, and thus translates into either insu cient or excessive exchange rate volatility relative to the e cient benchmark of policy cooperation (BB, and De Paoli 29a among others). However, in a global model, much of the potential gains from national policies are o set by the reaction of monetary authorities abroad. The noncooperative allocation turns out to be suboptimal for all. Despite strategic terms of trade manipulation, the deviations 8

9 from the cooperative allocation actually are quite small. 4 Indeed, gains from international policy coordination relative to Nash in the class of models we consider may be small they are actually zero for some con gurations of parameters ruling out cross-country spillovers relevant for policymaking, (see, e.g., Corsetti and Pesenti 25, extending this limiting result to LCP economies). The literature has recently emphasized these welfare results as a reason for skepticism about international policy cooperation (Obstfeld and Rogo 22, Canzoneri et al. 25). But the issue of gauging gains from cooperation is actually wide open, especially in the presence of real and nancial imperfections that may induce national central banks to play noncooperatively. Currency misalignments and international demand imbalances New directions for monetary policy analysis are emphasized in the last part of this chapter, which widens the scope of our inquiry to ine ciencies unrelated to nominal rigidities, stemming from arguably deeper and potentially more consequential distortions. Namely, we study monetary policy tradeo s in open economies where asset market distortions prevent the market allocation from being globally e cient. Speci cally, because of distortions resulting from incomplete markets, even if the exchange rate acts as a shock absorber moving only in response to current and expected fundamentals, its adjustment does not necessarily contribute to achieving a desirable allocation. On the contrary, it may exacerbate misallocation of consumption and employment both domestically and globally, corresponding to suboptimal ex post heterogeneity across countries. We rst show that, relative to the case of complete markets, both the Phillips curve and the loss function generally include a welfare-relevant measure of cross-country demand imbalances. This is the gap between marginal utility di erentials and the relative price of consumption which we dub the relative demand gap. Such a (theoretically consistent) measure of demand imbalances is identically equal to zero in an e cient allocation. A positive gap means that the Home consumption demand is excessive (relative to the e cient allocation) at the current real exchange rate (i.e., at the current relative price of consumption). With international borrowing and lending, in addition, demand imbalances are re ected by ine cient trade and current account de cits. 4 An open issue is the empirical relevance of terms-of-trade considerations in setting monetary policy a similar issue is discussed in the trade literature concerning the relevance of the optimal tari argument. 9

10 We then show that, with incomplete markets, optimal monetary policy has an international dimension similar to the case of LCP: domestic goals (output gap and in ation) are traded o against the stabilization of external variables, such as the terms of trade and the demand gap. A comparative analysis of these two cases however highlights di erences in the nature and size of the distortions underlying the policy trade-o s with external variables, suggesting conditions under which nancial imperfections are more consequential for the conduct of monetary policy, compared to nominal price rigidities in the import sector. We derive targeting rules showing that the optimal policy typically acts to redress demand imbalances containing the size of external de cits and/or correct international relative prices leaning against overvaluation of the exchange rate at the cost of some in ation. These targeting rules are characterized analytically for economies in nancial autarky. In these economies, as stressed by Helpman and Razin (1978), Cole and Obstfeld (1991) and Corsetti and Pesenti (21), a mechanism of risk sharing is provided by relative price adjustment a ecting the valuation of a country s output. Yet we show that no parameter con guration exists for which, in the presence of both productivity and preference shocks, equilibrium terms of trade movements automatically support an e cient allocation in the absence of trade in assets the equivalence between nancial autarky and complete markets is possible only for each of these shocks in isolation. We close the chapter by discussing the results in related work of ours (Corsetti, Dedola, and Leduc 29b) for an economy in which households can trade an international bond, suggesting that our analytical conclusions for the case of nancial autarky are a good guide to interpret the optimal policy in more general speci cations of the incomplete market economy. The text is organized as follows. In Part I, we assume complete markets, and analyze optimal policies in PCP and LCP economies under cooperation, as well as under Nash. In Part II, we allow for nancial imperfection, and discuss new policy trade-o s when nancial markets fail to support an e - cient allocation. Analytical details of the model and its solution are provided in a web appendix. 1

11 Part I Optimal stabilization policy and international relative prices with frictionless asset markets In this rst part of the chapter, we study optimal monetary policy in open economies in the context of a classical debate in international economics, concerning the extent to which exchange rate movements can redress the ine ciencies in the international adjustment mechanism created by nominal and monetary distortions, and foster desirable relative price adjustment across the border. To sharply focus on this issue, we follow much of the literature on the subject, and carry out our analysis assuming complete and frictionless asset markets. Under this assumption, we will contrast optimal policy prescriptions coherent with two leading views. One important view the classical view is that exchange rate movements are e cient (macro) shock absorbers, fostering relative price adjustment between domestic and foreign goods in response to aggregate shocks. By way of example, in response to a country-speci c positive supply shock, a fall in the international price of domestic output can e ciently occur via nominal and real depreciation, which lowers the foreign-currency prices of domestic exports while raising the domestic currency price of imports. Consistent with this view, a high sensitivity of the price of imports to the exchange rate imported in ation is a desirable manifestation of real price adjustment to macro disturbances. However, in the data, exchange rate movements appear to be only weakly re ected in import prices, not only at the retail level, but also at the border. The alternative view emphasizes that a high degree of stability in the prices of imports in local currency questions the very mechanism postulated by the classical view. To the extent that a low exchange rate pass-through re ects nominal rigidities that is, export prices are sticky in the currency of the destination market nominal depreciation does not lower the relative price of domestic goods faced by the nal buyers worldwide, hence it does not redirect demand towards them. A further dimension of the classical debate on the role of the exchange rate in the adjustment of international relative prices in the goods market concerns the possibility that countries engage in strategic manipulation of the terms of trade e.g. according to the logic of competitive devaluation. 11

12 In such case the market allocation would not be e cient because policymakers fail to internalize cross-border monetary spillovers. On the contrary, they intentionally use monetary instrument to exploit the monopoly power that a country may have on its terms of trade, and/or their ability to a ect relative prices. As a consequence, prices may be misaligned relative to the e cient allocation. In what follows, Section 2 will rst lay out our analytical framework. Section 3 and 4 will characterize optimal stabilization policy under the two contrasting views regarding the stabilizing properties of the exchange rate brie y discussed above. Section 5 will analyze a world equilibrium in the absence of international policy cooperation. 2 A baseline monetary model of macroeconomic interdependence 2.1 Real and nominal distortions in New Keynesian openeconomy analysis Our analysis builds on a two-country, two-good open-economy model which, by virtue of its analytical tractability, has become a standard reference for monetary analysis in international economics, at least since Obstfeld and Rogo (1995) the contribution starting the so-called New Open Economy Macroeconomics (an important precursor being Svensson and van Wijnbergen 1989). In the model, each economy is specialized in the production of one type of good supplied in many varieties, all traded across borders. Since the preferences of national consumers need not be identical, the consumption basket and therefore its price will generally be di erent across border. Even when the law of one price holds for each individual good/variety, the relative price of consumption that is, the real exchange rate will uctuate in response to shocks, and the purchasing power parity (PPP) will fail in general. In addition, nominal rigidities can also be envisioned to bring about deviations from the law of one price at the level of individual good variety. In that case, the relative price of imports and exports will not coincide with the terms of trade. In this workhorse model, nominal rigidities interact with three other sources of distortions. The rst is monopoly power in production, as in the (closed-economy) new-keynesian model. The other two are speci c to international analysis, and consists of incentives to deviate from globally optimal policies stemming from the assumption that countries have monopoly power 12

13 on their terms of trade, and imperfections in international nancial markets. In the rst part of the chapter, we will proceed under the assumption that nancial markets are complete so that the only policy trade-o s will be raised by distortions related to nominal rigidities and, when we look at noncooperative policies, a country s monopoly power on its terms of trade. The policy implications of nancial market imperfections will instead be analyzed in the second part of the chapter. In this section we will lay out the model in its general form, including features from which we will abstract in the course of our analysis, but could be useful for exploring generalization of our results. Namely, in our general setup we model a demand for money balances assuming that liquidity services provides utility. For comparison with the bulk of New-Keynesian analysis, however, our analysis of the optimal policy will proceed as if our economies were de facto cashless, ignoring this component of utility. Second, our general setup account for di erent degree of openness (asymmetric home-bias in demand) and country size (di erent population). To keep our exposition as compact as possible, however, Phillips curve and optimal policy will be derived imposing symmetry in these two dimensions. Finally, while our setup below explicitly accounts for the government budget constraint, in the rest of the chapter we will abstract from scal spending positing G =. 2.2 The setup The world economy consists of two countries, dubbed H (Home) and F (Foreign). It is populated with a continuum of agents of unit mass, where the population in the segment [; n) belongs to country H and the population in the segment (n; 1] belongs to country F. Each country specializes in one type of tradable good, produced in a number of varieties or brands with measure equal to population size Preferences and households decisions The utility function of a consumer j in country H is given by ( X 1 V j = E "U t C j t ; C;t + L M! j Z #) t+1 1 n ; P M;t V y t (h) ; t= t n Y;t dh : (1) 5 A version of the workhorse model with rm entry can build on Bilbiie Ghironi and Melitz (27). 13

14 Households obtain utility from consumption and the liquidity services of holding money, while they receive disutility from contributing to the production of all domestic goods y t (h) with a separable disutility. Variables C;t ; M;t ; Y;t denote country speci c shocks to preferences towards consumption, real money balances and production, respectively. Risk is pooled internally to the extent that agents participate in the production of all goods and receive an equal share of production revenue. We assume the following functional forms, widely used in the literature and convenient to obtain analytical characterizations (see, e.g., BB and CGG): 6 U C j t ; C;t C j1 t 1 = C;t 1 (2) L M j t+1 ; P M;t t! = M;t M j t+1 P t! V y t (h) ; Y;t = Y;t y t (h) Households consume both types of traded goods. So C t (h; j) and C t (f; j) are the same agent s consumption of Home brand h and Foreign brand f. For each type of good, we assume that one brand is an imperfect substitute for all other brands, with constant elasticity of substitution > 1. Consumption of Home and Foreign goods by Home agent j is de ned as: C H;t (j) C F;t (j) " 1 1= Z n n " 1 1= Z 1 1 n n # C t (h; j) 1 1 dh, (3) # 1 C t (f; j) 1 df The full consumption basket, C t, in each country is de ned by the following CES aggregator C = " 1 a 1= H C H + a 1= 1 F C F # 1 ; > : (4) 6 We follow BB in the functional form of the disutility of labor; it could be reconciled with CGG by assuming (1+) Y;t : 14

15 where a H and a F are the weights on the consumption of home and foreign goods, respectively, normalized to sum to 1, and is the constant elasticity of substitution between C H and C F. Note that this speci cation generates home bias if a H > 1 : Also, consistent with the assumption of specialization 2 in production, the elasticity of substitution is higher among brands produced within a country, than across types of national goods, that is, > : As well known, the utility-based CPI is: P t = ha H P H;t 1 + (1 a H ) P F;t 1 i 1 1 ; (5) where P H;t is the price sub-index for home-produced goods and P F;t is the price sub-index for foreign produced goods, both expressed in the domestic currency: P H;t 1 n Z n P t (h) dh ; PF;t 1 n Z n P t (f) df (6) Foreign prices, denoted with an asterisk like all the foreign variables, are similarly de ned. So, the Foreign CPI is: P t = h(1 a F) P H;t 1 + a FP F;t 1 i 1 1 : (7) Let Q t denote the real exchange rate, de ned as the relative price of consumption: Q t = E tpt. Even if the law of one price holds for each good P t individually (i.e., P t (h) = E t Pt (h) and P t (f) = E t Pt (f)), di erences in the optimal consumption baskets chosen by households imply that the price of consumption is not equalized across border. In other words, with di erent preferences, purchasing power parity (i.e., Q t = 1) will not hold. In addition to the real exchange rate, another international relative price of interest is the terms of trade, that is the price of imports in terms of exports. For the Home country, this can be written as T t = E t PH;t : From consumers preferences, we can derive household demand for a generic good h, produced in country H, and the demand for a good f, produced in country F : Pt (h) PH;t C t (h; j) = a H C j t P H;t P ; (8) t Pt (f) PF;t C t (f; j) = (1 a H ) C j t ; 15 P F;t P F;t P t

16 assuming the law of one price holds, total demand for good h and f can then been written as: " yt d Pt (h) PH;t (h) = P H;t " yt d Pt (f) PF;t (f) = P F;t P t P t a H C t + a H (1 a H ) # 1 n n Q t C t + G t (9) # n 1 n C t + Q t (1 a H) Ct + G t ; (1) where G t and G t are country-speci c government spending shocks, under the assumption that the public sector in the Home (Foreign) economy only consumes Home (Foreign) goods and has preferences for di erentiated goods analogous to the preferences of the private sector Budget constraints and Euler equations The individual ow budget constraint for the representative agent in the Home country can be generically written as: 7 Z M t +B H;t+1 + q H;t+1 (s t+1 ) B H;t+1 (s t+1 ) ds t+1 M t 1 +(1+i t )B H;t +B H;t R Pt (h)y t (h)dh + (1 t ) P H;t T t P H;t C H;t P F;t C F;t ; n where B H;t is the holdings of state-contingent claims, priced at q H;t, paying o one unit of domestic currency in the realized state of the world as of t, s t ; and i t is the yield on a domestic nominal bond B H;t, paid at the beginning of period t in domestic currency but known at time t 1, whose associated rst-order conditions result in the following familiar Euler equations: U C C t ; C;t = (1 + i t ) E t " U # C C t+1 ; C;t+1 ; (11) P t P t+1 determining the intertemporal pro le of consumption and savings. Likewise, from the Foreign country analogue we obtain: U C Ct ; " C;t = (1 + i t ) E t U C Ct+1 ; # C;t+1 : (12) P t P t+1 7 B H;t denotes the Home agent s bonds accumulated during period t 1 and carried over into period t. 16

17 The government budget constraints in the Home and Foreign economy are respectively given by Z Z Z t P t (h)y t (h)dh = P H;t ng t + + M j t M t 1 ; (13) t Z P t (f)y t (f)df = P F;t T j t Z (1 n) G t + Z T j t + M j t M t 1 : (14) Fluctuations in proportional revenue taxes t ( t ), or government spending G t (G t ), are exogenous and completely nanced by lump-sum transfers, T t (T t ), made in the form of domestic (foreign) goods Price-setting decisions Prices follow a partial adjustment rule à la Calvo-Yun. Producers of differentiated goods know the form of their individual demand functions and maximize pro ts taking overall market prices and products as given. In each period a fraction 2 [; 1) of randomly chosen producers is not allowed to change the nominal price of the goods they produce. The remaining fraction of rms, given by 1 chooses prices optimally by maximizing the expected discounted value of pro ts. When doing so, rms face both a domestic and a foreign demand. In principle, absent arbitrage across border, rms could nd it optimal to choose di erent prices. 8 Moreover, they may preset prices either in domestic or in foreign currency. Price setting under PCP The NOEM literature after Obstfeld and Rogo (1995) posits that prices are rigid in currency of the producers: rms set export prices in domestic currency, letting the foreign currency price of their product vary with the exchange rate. This hypothesis is dubbed producer currency pricing or PCP. Let P t (h) denote the price optimally chosen by the rm h for the domestic market at time t. To keep notation as simple as possible let fe t Pt (h)g denote the price chosen for the foreign market, expressed in domestic currency (under PCP, E t and Pt (h) move proportionally, as exchange rate pass through on import prices is complete). 8 See Corsetti and Dedola (25) for an analysis of optimal pricing under an no-arbitrage constraint. 17

18 The home rm s problem can then be written as follows 8 X 1 >< Max pt(h);etp t (h) E t f() s s= >:! P +E t p E t p t (h) H;t+s t (h) E t+s PH;t+s Pt+s V y t+s (h) ; Y;t+s U C;t+s (1 t+s ) " P t+s pt (h) PH;t+s (15) p t (h) (a H C t+s + G t+s) P H;t+s a H P t+s 3 1 n n C 5 t+s where revenues and costs are measured in utils and an asterisk denotes prices in Foreign currency. Let yt+s d (h) be the total demand of the good at time t + s under the circumstances that the prices chosen at t P t (h) and E t Pt (h) still apply at t + s. The rst-order conditions for this problems are X 1 E t () s UC;t+s P t (h) P s= t+s (1 t+s ) ( 1) V y y t+s d (h) ; Y;t+s " Pt (h) PH;t+s (a H C t + G t )#) = P H;t+s X 1 E t () s UC;t+s E t Pt (h) s= P t+s 2 4 E t Pt (h) E t+s PH;t+s P t+s (1 t+s ) ( 1) V y y t+s d (h) ; Y;t+s! 9 P = H;t+s P t+s a H 1 n n C t 3 5 ; = : Note that the last term on the left hand side of each condition is the demand for the good h in the Home and Foreign market, respectively, at the price chosen at time t these two terms indeed sum up to y d (h). Let t denote the markup charged by the rm t ( 1) (1 t+s ) which we assume subject to shocks due to time-varying taxes on producers t+s. The rm s problem is solved by E t 1 X s= () s UC;t+s P t;t+s P t (h) E t P t (h) = P t (h) t V y y d t+s (h) ; Y;t+s y d t+s = (16) for all h 18

19 As demand elasticities are constant and symmetric across borders, rms will optimally choose identical prices for both their domestic and their export markets: the law of one price will hold independently of barriers to good markets integration. The above solution hence implies E t P H;t = P H;t and P F;t = E t P F;t With PCP, it is easy to see that the terms of trade move one-to-one with the exchange rate, as well as with the domestic relative price of imports faced by consumers: T t = P F;t =E t P H;t = E tp F;t =P H;t = P F;t =P H;t. Since all the producers that can choose their price set it to the same value, we obtain two equations which describe the dynamic evolution of P H;t and P F;t : PH;t 1 = P 1 H;t 1 + (1 ) P t(h) 1 ; (17) F;t = PF;t (1 ) Pt (f) 1 : P 1 where denotes the probability that Foreign producers do not re-optimize prices during the period. Price setting under LCP The PCP assumption is questioned by an important strand of the literature (pioneered by Betts and Devereux 2), subscribing the alternative view that rms preset prices in domestic currency for the domestic market, and in foreign currency for the market of destination. This hypothesis is dubbed local currency pricing or LCP. Under this hypothesis, rms choose Pt (h) instead of E t Pt (h) and the rstorder condition for this price is E t 1 X s= () s UC;t+s E t+s Pt (h) P t V y yt+s d (h) ; Y;t+s t+s 2! P H;t+s 4 P t (h) P H;t+s P t+s a H 1 n n C t 3 9 = 5 ; = We assume that when a rm can re-optimize, it can do so both in the domestic and export markets. With LCP, for a rm not re-optimizing its price, exchange rate pass-through is zero. Let t denote deviations from the law of one price (LOOP): for the Home country, we can write H,t = E t P H;t =P H;t. As P H;t and P H;t are sticky, the law of one price is violated with any movement in the exchange rate. 19

20 Speci cally, nominal depreciation tends to increase the Home rms receipts in Home currency from selling goods abroad, relative to the Home market: nominal depreciation raises H,t. Because of deviations from the LOOP, the Home terms of trade T t = P F;t =E t PH;t will generally be di erent from the domestic price of imported goods, P F;t =P H;t. The dynamic evolution of the prices indexes P H;t, PH;t ; P F;t and P F;t is now described by four equations analogous to (17) International asset markets and exchange rate determination Exchange rate determination crucially di ers depending on the asset market structure. We contrast below the complete and the incomplete markets case, the latter including economies in nancial autarky, as well as economies with a limited number of assets traded across borders. Complete markets Under complete markets, price equalization in the state-contingent claims denominated in Home currency B H;t, implies the following equilibrium risk-sharing condition: U C C t+1 ; C;t+1 P t = U C Ct+1 ; C;t+1 E U C C t ; C;t P t+1 U C Ct ; t Pt C;t E t+1 Pt+1 : (18) Combined with the assumption of initially zero net foreign assets, this equation can be rewritten in the well-known form: Ct C;t P t = (C t ) C;t E t P t (19) For given Home and Foreign monetary policy, this equation fully determines the exchange rate in both nominal and real terms. A key feature of the complete-market allocation is that, holding preferences constant, Home per capita consumption can raise relative to Foreign per capita consumption only if the real exchange rate depreciates. 9 While we focus our analysis on symmetric economies, asymmetric pricing pattern are also plausible. A particularly interesting one follows the assumption that all export prices are preset in one currency, that is, a case of dollar pricing. Using our model, the case of dollar pricing can be modelled by combining the assumption of PCP for the rms in one country, and LCP for the rms in the other. Optimal policy with dollar pricing is analyzed by Devereux et al. (25) and Corsetti and Pesenti (28) see also Goldberg and Tille (28) for evidence. 2

21 Incomplete-market economy: nancial autarky In this alternative setup, the economy does not have access to international borrowing or lending. As only domestic residents hold the Home currency M t, the individual ow budget constraint for the representative agent j in the Home country is: R Pt (h)y t (h)dh M t M t 1 P H;t T t + (1 t ) P H;t C H;t P F;t C F;t : (2) n Barring international trade in asset, under nancial autarky the value of domestic production has to be equal to the level of public and private consumption in nominal terms. Aggregating private and public budget constraints, we have: Z P t C t = P t (h)y t (h)dh P H;t G t : (21) By the same token, the inability to trade intertemporally with the rest of the world imposes that the value of imports should equal the value of exports: np F;t C F;t = (1 n) E t P H;tC H;t: (22) Using the de nitions of terms of trade T t and real exchange rate Q t ; we can rewrite the trade balance condition in terms of aggregate consumption: n (1 a H ) T 1 t C t = (1 n) a HQ t C t : (23) For given monetary policy in the two countries, it is this equation balanced trade that determines exchange rates. Incomplete-market economy: trade in some assets Intermediate cases of nancial markets in between the two polar cases above can be modelled by allowing for cross-border trade in a limited number of assets. Home and Foreign agents hold an international bond, B H, which pays in units of Home currency and is zero in net supply. In addition they may hold other securities in the amounts it ; yielding ex post returns in domestic currency R it. The individual ow budget constraint for the representative agent in the Home country therefore becomes: 1 M t + B H;t+1 + X i i;t+1 M t 1 + (1 + i t )B H;t + X i i;t R i;t + (1 t ) R Pt (h)y t (h)dh n P H;t T t P H;t C H;t P F;t C F;t : (24) 1 B H;t and it denote the Home agent s assets accumulated during period t 1 and carried over into period t. 21

22 In this case, price equalization across internationally traded assets will imply the following modi ed risk-sharing condition: " E t U # " C C t+1 ; C;t+1 P t R i;t+1 = E t U C Ct+1 ; # C;t+1 E t+1 Pt+1 U C C t ; C;t P t+1 U C Ct ; C;t E t Pt R i;t+1 : (25) which holds for each individual asset (or portfolio of assets). The case of international trade in one bond is easily obtained from the above imposing it = : We stress two notable di erences between the complete-market and the incomplete-market economy. First, while exchange rates re ect only shocks to fundamentals (thus acting as shock absorber ) in both economies, when markets are incomplete their equilibrium value will di er from the e cient one, irrespective of nominal rigidities, due to this form of asset market frictions. A second important di erence in the equilibrium allocation with complete and incomplete markets is that international risk sharing will generally be imperfect, resulting in ine cient uctuations in aggregate demand across countries, as shocks open a wedge between national wealth. Let D t denote the welfare-relevant cross-country demand imbalance, de ned as the following PPP-adjusted measure of cross-country demand di erential: Ct 1 C;t D t = (26) Q t C;t C t By (19), under complete markets D t is identically equal to one regardless of the shocks hitting the economy. With incomplete markets, instead, D t will generally uctuate ine ciently contingent on shocks. 11 Because of ine cient relative prices and cross-country demand uctuations, we will see below that optimal monetary policy will di er across structures of international asset markets. 2.3 Natural and e cient allocations (Benchmark exibleprice allocations) Allocations under exible prices provide natural benchmarks for comparison across di erent equilibria under sticky prices. Without nominal rigidities, 11 Viani (21) provides a theoretical and empirical analysis of D t. 22

23 the price setting decisions simplify to: U C C t ; C;t P H;t P t = C;t Ct P H;t = P t ( 1) (1 t ) V y ( 1) (1 t ) PH;t! a H C t + a 1 n H n Q t C t + G t ; Y;t 1 a H C t + a H 1 n n Q t C t + G t C (27) A P t PH;t P t Y;t U C Ct ; PF;t C;t Pt C;tCt PF;t Pt = = ( 1) (1 t )V y ( 1) (1 t ) PF;t n (1 a H ) 1 n C t + Q t (1 a H) Ct + G t ; Y; 1 (1 a H ) n 1 n Q t C t + (1 a H ) C t + G t C : ( A P t P F;t Pt Y;t whereas, holding the law of one price, the terms of trade and the real exchange rate can be written as follows : T t = P F;t P H;t Q 1 t = a H P H;t 1 + (1 a H ) P F;t 1 a H P H;t 1 + (1 a H ) P F;t 1 = a H + (1 a H ) T t 1 a H + (1 a H ) T t 1 ; Throughout the chapter, the model s equilibrium conditions and constraints will be written out in log-deviations from steady-state assuming that in steady-state the net foreign asset position is zero. Denoting with an upper-bar steady-state values, bx t = ln x t =x will represent deviations under sticky prices, while ex t = ln x t =x will represent deviations under exible prices. Recalling that denote the equilibrium markup ( t = = (( 1) (1 t ))), a log-linear approximation around the steady-state of 23

24 the above equations will yield: b C;t C e t (1 a) T e t = 6 4 b C;t C e t + (1 a ) T e t = 6 4 eq t = (a + a 1) T e t (29) 2 3 Y G bg t b b t Y;t + (1 a) Y G et Y Y t + 2 a H + (1 a H ) T 1 1 a H C bg t Y G Y b Y;t a H T 1 t + (1 a H ) 1 where a, a,y, Y, G, and G are de ned as follows: 1 a = a H + 1 a H a H T 1 ; 1 a = (1 a H ) T 1 a H + (1 a H ) T 1 bg t = G t G ; Y = ha H + (1 a H ) T 1 i 1 Y bg t = G t G Y ; Y = h i a HT 1 + (1 a 1 H) e C Y t + a H C Q 1 n ec Y n t + Q e t b t (1 a ) Y G e Y Tt (1 a H) CQ n ect Y 1 n Q e 1 t + (1 a H ) C e A Y Ct a H C + 1 n n To solve for the world competitive allocation, we need a further equation, characterizing exchange rate determination. As discussed above, the equilibrium will crucially di er depending on the structure of international nancial markets. With complete markets, the relevant equation is (19), which in log-linearized form becomes eq t = b b C;t C;t + ect C e t (3) For the case of nancial autarky, instead, the relevant equation is (23), which becomes eq t = a + a 1 ect C e (a + a) 1 t (31) Observe that, relative to the case of complete markets (19), the real exchange rate is still proportional to the ratio of consumption across countries. Yet, under nancial autarky, the proportionality coe cient, rather than being equal to the (inverse of the) intertemporal elasticity, is a function of ; the trade elasticity, and of a H, the degree of home bias in consumption. 24 a HC Q + G n 1 n (1 a H) Q C + (1 a H) C : + G